Estimation of treatment effects on ordinal variables in multivariate ordered choice models
DOI:
https://doi.org/10.22394/1993-7601-2026-81-68-92Keywords:
иерархическая система уравнений, многомерная порядковая пробит модель, эндогенность, неслучайный отбор, эффекты воздействия, аддиктивные блага, стрессAbstract
The current estimation of treatment effects on ordinal variables when the conditional independence assumption between the treatment variable and the outcome variable is violated. An extension of existing approaches is proposed through a parametric method based on a hierarchical system of ordered choice equations. The key methodological contribution involves deriving analytical formulas for calculating average treatment effects and average marginal effects of explanatory variables within multivariate ordered probit models that account for endogenous treatment and non-random selection in ordinal outcomes. Using NSDUH survey data (2020–2023), we empirically analyze stress effects on addictive goods consumption. The analysis demonstrates a significant impact of stress on the propensity for addictive behavior. It also assesses the treatment effects of different levels of stress on the probability and frequency of substance use. A comparative analysis with models that ignore endogeneity confirms the necessity of an estimation hierarchical system for exact measurement of the stress effect. Substance use probability increases consistently with stress levels, with women exhibiting greater vulnerability to these effects. The study shows that stress impact varies across socioeconomic groups, identifying specific high-risk populations for substance use initiation.Downloads
References
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Chesher A., Rosen A. M., Siddique Z. (2025). Estimating endogenous effects on ordinal outcomes. Review of Economics and Statistics, 107 (6), 1667–1683. DOI: 10.1162/rest_a_01348.
Chesher A., Smolinski K. (2012). IV models of ordered choice. Journal of Econometrics, 166 (1), 33–48. DOI: 10.1016/j.jeconom.2011.06.004.
Cleck J. N., Blendy J. A. (2008). Making a bad thing worse: Adverse effects of stress on drug addiction. The Journal of Clinical Investigation, 118 (2), 454–461. DOI: 10.1172/JCI33946.
De Goeij M. C., Suhrcke M., Toffolutti V., van de Mheen D., Schoenmakers T. M., Kunst A. E. (2015). How economic crises affect alcohol consumption and alcohol-related health problems: A realist systematic review. Social Science & Medicine, 131, 131–146. DOI: 10.1016/j.socscimed.2015.02.025.
Fergusson D. M., Boden J. M., Horwood L. J. (2011). Structural models of the comorbidity of internalizing disorders and substance use disorders in a longitudinal birth cohort. Social Psychiatry and Psychiatric Epidemiology, 46 (10), 933–942. DOI: 10.1007/s00127-010-0268-1.
Gfroerer J. C., Larson S. L., Colliver J. D. (2007). Drug use patterns and trends in rural communities. The Journal of Rural Health, 23 (1), 10–15. DOI: 10.1111/j.1748-0361.2007.00118.x.
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Han S., Vytlacil E. J. (2017). Identification in a generalization of bivariate probit models with dummy endogenous regressors. Journal of Econometrics, 199 (1), 63–73. DOI: 10.1016/j.jeconom.2017.04.001.
Horwood L. J., Fergusson D. M., Coffey C., Patton G. C., Tait R., Smart D., Letcher P., Silins E., Hutchinson D. M. (2012). Cannabis and depression: An integrative data analysis of four Australasian cohorts. Drug and Alcohol Dependence, 126 (3), 369–378. DOI: 10.1016/j.drugalcdep.2012.06.002.
Imbens G. W. (2004). Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics, 86 (1), 4–29.
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Knaus M. C., Lechner M., Strittmatter A. (2021). Machine learning estimation of heterogeneous causal effects: Empirical Monte Carlo evidence. The Econometrics Journal, 24 (1), 134–161. DOI: 10.1093/ectj/utaa014.
Lederbogen F., Kirsch P., Haddad L., Streit F., Tost H., Schuch P., Wüst S., Pruessner J. C., Rietschel M., Deuschle M., Meyer-Lindenberg A. (2011). City living and urban upbringing affect neural social stress processing in humans. Nature, 474 (7352), 498–501. DOI: 10.1038/nature10190.
Madden D. (2008). Sample selection versus two-part models revisited: The case of female smoking and drinking. Journal of Health Economics, 27 (2), 300–307. DOI: 10.1016/j.jhealeco.2007.07.001.
Manthey J., Hassan S. A., Carr S., Kilian C., Kuitunen-Paul S., Rehm J. (2021). Estimating the economic consequences of substance use and substance use disorders. Expert Review of Pharmacoeconomics & Outcomes Research, 21 (5), 869–876. DOI: 10.1080/14737167.2021.1916470.
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Negrao A., Deuster P., Gold P., Singh A., Chrousos G. (2000). Individual reactivity and physiology of the stress response. Biomedicine & Pharmacotherapy, 54 (3), 122–128. DOI: 10.1016/S0753-3322(00)89044-7.
Peltier M. R., Verplaetse T. L., Mineur Y. S., Petrakis I. L., Cosgrove K. P., Picciotto M. R., McKee S. A. (2019). Sex differences in stress-related alcohol use. Neurobiology of Stress, 10, 100149. DOI: 10.1016/j.ynstr.2018.100149.
Rubin D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66 (5), 688–701. DOI: 10.1037/H0037350.
Ruhm C. J., Black W. E. (2002). Does drinking really decrease in bad times? Journal of Health Economics, 21 (4), 659–678. DOI: 10.1016/s0167-6296(02)00033-4.
Ruisoto P., Contador I. (2019). The role of stress in drug addiction. An integrative review. Physiology & Behavior, 202, 62–68. DOI: 10.1016/j.physbeh.2019.01.022.
SAMHSA (2024). Key substance use and mental health indicators in the United States: Results from the 2023 National Survey on Drug Use and Health. HHS Publication No. PEP24-07-021, NSDUH Series H-59. Center for Behavioral Health Statistics and Quality. https://www.samhsa.gov/data/report/2023-nsduh-annual-national-report.
Sinha R. (2008). Chronic stress, drug use, and vulnerability to addiction. Annals of the New York Academy of Sciences, 1141 (1), 105–130. DOI: 10.1196/annals.1441.030.
Smith V. K., Taylor Jr. D. H., Sloan F. A., Johnson F. R., Desvousges W. H. (2001). Do smokers respond to health shocks? Review of Economics and Statistics, 83 (4), 675–687.
Sorge J. T., Young M., Maloney-Hall B., Sherk A., Kent P., Zhao J., Stockwell T., Perlova K., Macdonald S., Ferguson B. (2020). Estimation of the impacts of substance use on workplace productivity: A hybrid human capital and prevalence-based approach applied to Canada. Canadian Journal of Public Health, 111 (2), 202–211. DOI: 10.17269/s41997-019-00271-8.
Torres O. V., O’Dell L. E. (2016). Stress is a principal factor that promotes tobacco use in females. Progress in Neuro-Psychopharmacology and Biological Psychiatry, 65, 260–268. DOI: 10.1016/j.pnpbp.2015.04.005.
Verplaetse T. L., Peltier M. R., Roberts W., Pittman B., McKee S. A. (2021). Gender and past year serious psychological distress are associated with past year AUD: Time-varying results from the National Survey on Drug Use and Health (NSDUH; 2008–2017). Addictive Behaviors, 116, 106815. DOI: 10.1016/j.addbeh.2020.106815.
Vytlacil E. (2006). Ordered discrete-choice selection models and local average treatment effect assumptions: Equivalence, nonequivalence, and representation results. The Review of Economics and Statistics, 88 (3), 578–581. DOI: 10.1162/rest.88.3.578.
